Cook over medium heat, stirring often, until the mixture thickens and becomes jam-like, about 10-15 minutes. Set aside to cool.
Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.
Lightly flour a clean surface and roll out the puff pastry sheets slightly with a rolling pin. Cut each sheet into 6 even squares (12 squares total) using a pizza cutter or sharp knife.
Spoon about 2 tablespoons of the cooled strawberry mixture onto the center of each square.
Fold one corner over to the opposite corner to form a triangle. Press the edges together with a fork to seal tightly. Use a sharp knife to cut a small slit in each one to allow steam to escape.
Arrange the turnovers on the prepared baking sheet, leaving space between them. Beat the egg with 1 tablespoon of water and brush over the tops of the turnovers for a golden finish.
1 medium egg
Bake for about 20 minutes, or until the pastries are puffed and golden brown.
For the glaze, whisk together the powdered sugar, vanilla extract, and milk in a medium bowl until smooth. Adjust the consistency by adding more milk for a thinner glaze or more powdered sugar for a thicker glaze.